As far as players with previous character issues, we've brought those guys in before. Chris Morris wasn't a coaches dream with the Nets when Utah signed him (Chuck Daly who previously coached Morris even dissed him when speaking about the failed trade that would've sent Morris to Daly's Magic in '98). We brought David Benoit back in 2000 after he was already out of the league due to a drinking problem. We pursued and signed John Starks who wasn't an easy player to coach and had spent the previous 2 seasons pouting in Golden State. DeShawn Stevenson wasn't a choir boy at Washington Union. In 2003 we traded for Keon Clark and gave him a shot even though he was one of the biggest potheads in the league (and the Jazz had an even younger team in '03 than they do now) and a few years later we drafted Robert Whaley despite being charged with statutory rape in HS and battery in college.
The Jazz have rolled the dice on players with character issues in the past, and that can work as long as you don't have too many of them on the team (this all goes along with a leadership philosophy called the "Law of Threes").
The important thing in this is the message you send when somone screws up. The Jazz have shown that they'll give people opportunities, but they're not going to tolerate any BS.